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                [Usaco2016 Dec]Team Building                </h1>
                <p>时间限制：10s&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  空间限制：128MB</p>			</div>
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                                <h3>题目描述</h3><p><div>Every year, Farmer John brings his NN cows to compete for &quot;best in show&quot; at the state fair. His arch</div>
<div>-rival, Farmer Paul, brings his MM cows to compete as well (1&le;N&le;1000,1&le;M&le;1000).Each of the N+MN+</div>
<div>M cows at the event receive an individual integer score. However, the final competition this year wi</div>
<div>ll be determined based on teams of KK cows (1&le;K&le;10), as follows: Farmer John and Farmer Paul both&nbsp;</div>
<div>select teams of KK of their respective cows to compete. The cows on these two teams are then paired&nbsp;</div>
<div>off: the highest-scoring cow on FJ's team is paired with the highest-scoring cow on FP's team, the s</div>
<div>econd-highest-scoring cow on FJ's team is paired with the second-highest-scoring cow on FP's team, a</div>
<div>nd so on. FJ wins if in each of these pairs, his cow has the higher score.Please help FJ count the n</div>
<div>umber of different ways he and FP can choose their teams such that FJ will win the contest. That is,</div>
<div>&nbsp;each distinct pair (set of KK cows for FJ, set of KK cows for FP) where FJ wins should be counted.&nbsp;</div>
<div>Print your answer modulo 1,000,000,009.</div>
<div>
<div>每年农夫约翰都会带着他的N只牛去集会上参加&ldquo;你是最棒哒&ldquo;的比赛。他的对手农夫保罗也带了M只牛去参加比赛</div>
<div>(1 &le; N &le; 1000, 1 &le; M &le; 1000)。每只牛都有自己的分数。两人会选择K只牛组成队伍(1 &le; K &le; 10)，两队</div>
<div>牛在按分数大小排序后一一配对，并且约翰打败保罗当且仅当对于每一对牛，约翰的牛分数都比保罗的高。请帮助</div>
<div>约翰计算约翰打败保罗的方案数 mod 1000000009。两种方案不同，当且仅当约翰或保罗选择的牛的集合与另一种</div>
<div>方案不同。</div>
</div>
<div></div>
<p></p></p><hr/><h3>输入格式</h3><p><div>The first line of input contains N, M, and K. The value of K will be no larger than N or M.</div>
<div>The next line contains the N scores of FJ's cows.</div>
<div>The final line contains the M scores of FP's cows.</div>
<div></div>
<p></p></p><hr/><h3>输出格式</h3><p><div>Print the number of ways FJ and FP can pick teams such that FJ wins, modulo 1,000,000,009.</div>
<div></div>
<p></p></p><hr/><h3>样例输入</h3><pre>10 10 3
1 2 2 6 6 7 8 9 14 17
1 3 8 10 10 16 16 18 19 19</pre><hr/><h3>样例输出</h3><pre>382</pre><hr/><h3>提示</h3><p>没有写明提示</p><hr/><h3>题目来源</h3><p>Platinum 鸣谢Firstlast提供译文</p>
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